Ultimate Load Behaviour of Steel-Concrete Composite Plate Girders with Inclined Stiffeners

This paper focuses on the ultimate load behaviour of steel-concrete composite plate girders with inclined stiffeners. For this research, non-linear modelling and analyses were carried out on ten simply supported composite plate girders using a commercial finite element software, LUSAS. The girders are of practical design size and subjected to a single concentrated load applied at the centre of the girder span. Effects of different inclination angles of intermediate stiffeners and web-depth to thickness (d/t) ratios on the post-buckling behaviour of the girders are investigated. Five different angles of stiffeners, measured from the bottom flange, were considered in the research, viz., 90°, 75°, 60°, 45° and 30° while the web thickness, tw used in this study are 2 mm and 3 mm. With the effects of such inclinations, the variations of ultimate load, load-deflection response and failure characteristics were obtained. The load carrying capacity was found to rise significantly of about 32%, as the angle of inclination reduced from 90° to 30°. The ultimate strength of the composite girder also shows a maximum increase of 28%, when the web thickness, tw rises from 2 mm to 3 mm.


INTRODUCTION
In civil engineering applications, when a hot-rolled steel I-beam is insufficient to resist the high bending moment or shear loading over a long span, a built-up plate girder is employed to satisfy the serviceability of the required section.This built-up plate girder is geometrically fabricated like those of steel I-beam sections.These built-up plate girders are designed to resist the bending moment with their flanges, while, the shear stresses are carried by the web panels.
In general, slender webs in plate girders exposed to local buckling and relatively low shear need to be strengthen to prevent web buckling.Application of intermediate horizontal stiffener has been used to prevent the torsion of flange and also serves as a boundary for the tension field action on the web.The stability of web plates can also be enhanced by dividing individual panels using longitudinal stiffeners.The related study was conducted by Evans and Porter (1978), Horn and Grayson (1983), and Alinia and Moosavi (2008) in the past to determine the number, dimensions, and positioning of longitudinal stiffeners within a particular web panel to provide optimum performance for steel plate girders.
Intermediate stiffener applications are not limited to horizontal or longitudinal positioning, but also can be applied in an incline manner.The study of incline stiffeners for steel plate girders was carried by Antoni (1941) and Guarnieri (1985) where they have listed their advantages.It can be concluded from the test series by Antoni (1941) and Guarnieri (1985), the incline stiffeners have the advantage of limiting the shear factor without the need for additional longitudinal stiffeners.Test results conducted by Azmi et al. (2017) also shows significant increase in the ultimate strength of girders to the extent of 38% as the angle of inclination of stiffeners are reduced, which is quite significant in today's construction requirement.
The need for cost-effective construction with satisfactory performance has led to the use of composite action between the steel girder and concrete slab.These two structural elements in a typical composite construction are firmly connected together through shear connectors so that they can act compositely as a single unit, thus fully exploiting the advantages of the two different materials.The performance of a composite plate girder is determined by the individual strength of concrete slab and steel girder as well as shear connection stiffness between the interacting elements.
Theoretically, the ultimate strength analysis of conventional steel plate girders includes the advantage of tensile action in the web plate (Allison et al. 1982).When the plate girder is subjected to shear force action, the band strain in the web width becomes uneven due to the change in the plastic hinge location.Consequently, when concrete slabs are added to the compressive or tension flange, the position of the plastic hinge formation may differ from the usual steel girder (Baskar & Shanmugam 2003).Due to this, it can be concluded that the plate girder in composite construction behaves differently from a conventional steel plate girder as a result of composite action between steel girder and concrete slab.
In addition, plate girders are usually designed by neglecting the strength contribution of the concrete slab and focus only on the plate girder itself.If the composite interaction with concrete slab is taken into account, the plates of the plate girder can be minimized in design and thus provide the necessary cost-saving alternatives needed.The use of inclined stiffeners will also cause the behaviour of the girder to be complex and therefore, a series of analysis on the ultimate load behaviour of steel-concrete composite plate girders with inclined stiffeners must be performed to investigate the overall behaviour of the girder.
For this research, non-linear finite element investigation on such girders has been undertaken using a finite element package.Attention is focused on aspects such as inclination angle of the stiffeners as well as the web thickness to highlight the benefits of using inclined stiffeners over the conventional stiffeners.Details of the numerical modelling are reported herein along with the results obtained.

FINITE ELEMENT ANALYSIS FINITE ELEMENT MODEL
Three-dimensional finite element models were developed by using LUSAS package.Non-linear analyses were carried out on 10 composite plate girder models having different degrees of inclined stiffeners and web thickness.These girders are basically modified from the girder CPG 7 tested in the past by Baskar and Shanmugam (2003) in order to achieved the objectives of the study.Stiffeners were placed accordingly on both sides of the web plate, thus subdividing the thin web into four web panels.Vertical stiffeners are placed at the mid-span to prevent premature failure due to local buckling.Material properties for steel and concrete slab were also obtained from Baskar and Shanmugam (2003).The mechanical properties of the material used for the composite girder is given in Table 1.Notation such as E s and E c represents the Young's Modulus for steel and concrete respectively, while f y(avg) is the average yield stress for steel, f cu and f t are the cube compressive strength and split tensile strength respectively.These values are necessary in simulating the real life properties of the composite girder in the research.
Five different angles of intermediate stiffeners, measured from the bottom flange, were considered in the research, viz., 90°, 75°, 60°, 45° and 30° while the web thickness, t w used are 2 mm and 3 mm which represents different web slenderness ratio, d/t w .The concrete slab dimensions used for this study are 1200 × 1500 mm, where the connection between the concrete slab is considered a full shear connection.The basic dimensions were kept the same in all girders in order to have a constant span length, L = 4796 mm, depth of web panel, d = 750 mm, length of web panel, b = 1141 mm, flange width, b f = 160 mm, flange thickness, t f = 10 mm and aspect ratio, b/d = 1.5.Details of the models developed for verification the present study, and the corresponding material properties are presented in Table 2.
The test specimens are noted in the text as CPG-90-2, CPG-90-3, CPG-75-2, CPG-75-3, CPG-60-2, CPG-60-3, CPG-45-2, CPG-45-3, CPG-30-2 and CPG-30-3.The CPG notation is used to represent the composite plate girder while the 90, 75, 60, 45, and 30 markings refer to the value of the inclination angle of the intermediate stiffener measured from the bottom of the plate girder.Notation 2 and 3 refer to the web thickness, t w of 2 mm and 3 mm respectively.Figure 1 shows the front view and the cross section of a sample study model.flexural and transverse shear deformations which are suitable for thin wall applications.The formulation of this element is consistent with tangent stiffness and the selection of visible elements is more effective for models with non-linear geometries.Before QSL8 element is used in the models, line mesh elements need to be used, to divide into several parts to ensure that only the four side elements will be generated.

MESH
Regular finite element mesh with division size of 50 × 50 mm was adopted in all analysis.It was chosen based on the study of convergence conducted by Basher et al. (2009) to determine the optimum size of elements that can produce quite precise solutions in terms of strength and behaviour with acceptable calculations.A typical mesh used in this analysis is shown in Figure 2. The steel plate and concrete slab for the composite girder were modelled as isotropic elastic-perfectly plastic materials, giving a uniaxial stress-strain relationship.Parameters need to define the potential stress model of the material as listed in Table 2.The Poisson and steel ratio are 0.3 and 0.2 respectively.Non-linear characteristics are based on the Von-Mises yielding criteria that represent the ductile behaviour of steel material which exhibits a slight volumetric strain while the concrete uses the Von-Mises variable criterion.

BOUNDARY CONDITION AND LOADING
Boundary conditions were imposed to the finite element model to reflect simple support conditions i.e., pin and roller.At the pin support, the girder was restrained against the displacements in global x-, y-and z-directions but free to move along z-direction at the roller support.Nevertheless, rotations about all directions were allowed for in both types of support conditions.A vertical concentrated load was applied to the girder incrementally.In LUSAS, the convergence criterion is based on force and displacement.An automatic load increment with Crisfield's arc length control was selected.
The load step reduction with specified reduction factor and increase factors of 0.5 and 2.0 respectively was chosen.This procedure will assist in stepping over a difficult point in the analysis so that the solution can proceed to lead to convergence.Termination of analysis was, however, limited to the default criteria.

ULTIMATE LOAD CAPACITY OF MODEL
It is crucial to validate the models before carrying out further analysis.The assessment of the accuracy was made through comparisons between the finite element predictions and the corresponding experimental results for the girders CPG 7 (Baskar & Shanmugam 2003) and CPG 8 (Baskar & Shanmugam 2003).Finite element analysis provided a detailed output from which the ultimate loads and deformation behaviour can be extracted.Finite element results for ultimate load, P u , FEM is tabulated in Table 3 along with the corresponding experimental values, P u, exp .It is apparent from the ratio P u , FEM / P u, exp that the finite element and experimental values are relatively close within acceptable level of accuracy, i.e., ±10%.Thus, it can be concluded that the proposed finite element model is capable of predicting the ultimate strength of steel plate girders with good approximation.
The finite element modelling results for ultimate loading are shown in Tables 4 and 5 (comparison with respective inclination angle of stiffener).The result obtained indicates that the ultimate strength value of the composite girder will increase if the inclination angle of intermediate stiffener, θ decreases from 90° to 30°.For example, for a composite girder with a web thickness of t w = 2 mm, the ultimate strength will increase by 32% when the inclination angle decreases from 90° (girder CPG-90-2) to 30° (girder CPG-30-2), while the ultimate strength will increase by 20% when the inclination angle increases from 90° to 30° (comparison between girders CPG-90-3 and CPG-30-3) for a girder with a web thickness of t w = 3 mm.Incline intermediate stiffener is found to be able to withstand part of the burden imposed on the composite girder through the redistribution of forces in the web members formed from the stiffener positioning.This is attributed to the formation of a web-shaped trapezoid panel.The tensile field width in the web panel will also be larger with the presence of these stiffeners, which in turn causes the web panel to be able to bear higher tensile strength compared to the girder that has a quadrilateral-shaped panel.
In addition, the difference due to the web thickness for ultimate loadings are shown in Table 5.It is observed that the ultimate loading increases as the respective web thickness increases.For example, a composite girder with an inclination intermediate stiffener of θ = 90°, has shown an ultimate strength increase of 28% when the web thickness, t w rises from 2 mm to 3 mm (comparing girders CPG-90-2 and CPG-90-3), while inclination angle of 75°, 60°, 45° and 30° shows the final load increase of 26%, 23%, 17% and 17% (CPG-75-2 and CPG-75-3, CPG-60-2 and CPG-60-3, CPG-45-2 and CPG-45-3, CPG-30-2 and CPG-30-3).This behaviour is associated with the web slenderness ratio, (d/t w ), where a high value of it will give opposing slender reaction, thus giving a high ultimate load value Load-deflection plots obtained from the finite element analysis are presented in Figures 3(a) -(e), which is group based on inclination angle similarities.The curves represent mid-span deflection plotted against the applied load, primarily the bending behaviour of the girders.From the plotted graphs, it is found that at the initial stage of the applied load, the deflection in the middle of the span will be linearly proportional.The value of the applied load increases and then the curve of the graph will show non-linearity in its curve when it has reached the point of yielding.Then, when the load is increased consistently, the relationship between the load-deflection will indicate that the phase is non-linear.
The bending on the web panel of the girder will increase as a result of the formation of tension fields and the plastic hinges formation on the top and bottom of the flange, which is needed to achieve the final load.The composite action will cause the tension band to increase due to the connection with the concrete slab itself.Hence, the load value will be slowly decreased after the ultimate load capacity has been achieved.Girders with lower inclination angle indicate a higher bending stiffness as shown in the gradient of the curve in the elastic phase (Figures 3(a) -(e)).This proves that there is an advantage in the use of incline stiffeners that can be used as offset of the loss of shear strength in the composite girder effectively.From all plotted graphs, it shows that the bending behaviour of all modelling girders with the load capacity will decrease when the web slenderness ratio is greater.This is attributed to the web-to-depth ratio as mentioned earlier.
Apart from that, it is found that all of the curve show ductility behaviour, where the girder fails in large bending.This is due to the low tensile field being generated on web plates due to the application of concrete slabs that form a composite strength between plate girder and concrete slab, which is expected in typical composite girder.Based on the finite element modelling, the point load has been applied in the mid-span for each modelling girder.When the applied load has reached a critical buckling load value, diagonal buckling will be formed in every web panel of the girder modelling.All girders show the same behaviour when it has reached this phase.Increased load in the post-buckling phase will be corrected by the tension membrane reaction and will result in increased deformation of the web outside the plane.In this phase, the increase in applied load will cause greater vertical deflection when compared to the elastic phase due to the decrease in flexural stiffness.Furthermore, from the plotted contours, the stress intensity on the concrete slab at the center of the girder clearly shows that the girder has been subjected to high compressive strength under bending.The plotted contours also show compressive stresses for girders that have inclined intermediate stiffeners are higher than those with vertical intermediate stiffener.

CONCLUSION
Non-linear finite element analysis has been carried out on simply supported thin-webbed plate steel-concrete composite plate girders with inclined intermediate stiffeners.Results have shown the variations of ultimate strength and behaviour at failure.Different degrees of inclination angles of the stiffeners, θ and web thickness, t w which represent different web-depth to thickness (d/t w ) ratios.It can be concluded from the findings that use of inclined stiffeners affects significantly the load carrying capacity of composite plate girders.This preliminary study has, therefore, provided some general insights regarding the ultimate load behaviour of plate girders having inclined stiffeners and thus, further analysis on stiffeners with inclination angle lower than 30° may be undertaken.In addition, experimental investigations and detailed theoretical works are strongly recommended.
FIGURE 3. Relationship between load-deflection responses based on the same inclination angle, θ but different in thickness of web, t w

FIGURE 5 .
FIGURE 5. Tension field formations formed in the web panels of composite girders at ultimate loading

TABLE 1 .
Mechanical properties of steel and concrete materials ELEMENTVarious types of elements are available in the LUSAS element library.Proper selection of elements is important as they dictate the behaviour of the model.The geometries of web, flanges, and stiffeners and concrete slab were meshed with three-dimensional quadrilateral shell elements (QSL8).Each of the elements consists of four corner and four intermediate nodes.The element formulation takes account of membrane,

TABLE 2 .
Details of test girders FIGURE 1. Elevation and sections of a typical test girder FIGURE 2. Typical finite element mesh 62 MATERIAL MODEL

TABLE 3 .
Verification of numerical model

TABLE 6 .
Difference in ultimate loading in reference to web thickness